SOLUTION: 2. A professor started a project with a group of students, 60% of whom were boys. Due to some unavoidable reasons, six girls couldn't turn up, so the professor had to make some cha

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: 2. A professor started a project with a group of students, 60% of whom were boys. Due to some unavoidable reasons, six girls couldn't turn up, so the professor had to make some cha      Log On

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Question 80652: 2. A professor started a project with a group of students, 60% of whom were boys. Due to some unavoidable reasons, six girls couldn't turn up, so the professor had to make some changes in the group. He admitted six boys. In doing so, the percentage of boys in the project increased to 75%. Find the number of boys and girls involved in the project initially.
Answer by ankor@dixie-net.com(15652) About Me  (Show Source):
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A professor started a project with a group of students, 60% of whom were boys. Due to some unavoidable reasons, six girls couldn't turn up, so the professor had to make some changes in the group. He admitted six boys. In doing so, the percentage of boys in the project increased to 75%. Find the number of boys and girls involved in the project initially.
:
Let t = total number of students,
.6t = number of boys originally
:
(.6t + 6) = actual number of boys (which the problem says became 75%)
:
From all this we have one simple equation:
.6t + 6 = .75t
.6t - .75t = -6
-.15t = -6
t = -6/-.15
t = +40 kids
:
.6 * 40 = 24 boys originally
.4 * 40 = 16 girls "